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The midpoint MM of VW\overline{VW} has coordinates (9,4)(9,\,4). Point WW has coordinates (10,8)(10,\,8). Find the coordinates of point VV.\newlineWrite the coordinates as decimals or integers.\newlineV=(_,_)V = (\_,\,\_)

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Q. The midpoint MM of VW\overline{VW} has coordinates (9,4)(9,\,4). Point WW has coordinates (10,8)(10,\,8). Find the coordinates of point VV.\newlineWrite the coordinates as decimals or integers.\newlineV=(_,_)V = (\_,\,\_)
  1. Understand Midpoint Formula: Understand the midpoint formula and the given information.\newlineThe midpoint formula for a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is (x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right). We are given the midpoint M(9,4)M(9, 4) and one endpoint W(10,8)W(10, 8). We need to find the coordinates of the other endpoint V(x1,y1)V(x_1, y_1).
  2. Set Up Equations: Set up the equations for the midpoint based on the given information.\newlineThe midpoint MM is the average of the coordinates of VV and WW. Therefore, we have the following equations:\newline(9,4)=(x1+102,y1+82)(9, 4) = \left(\frac{x_1 + 10}{2}, \frac{y_1 + 8}{2}\right)
  3. Solve for x-coordinate: Solve for the x-coordinate of point V.\newlineUsing the x-coordinate of the midpoint, we have:\newline9=x1+1029 = \frac{x_1 + 10}{2}\newlineMultiply both sides by 22 to clear the fraction:\newline18=x1+1018 = x_1 + 10\newlineSubtract 1010 from both sides to solve for x1x_1:\newlinex1=1810x_1 = 18 - 10\newlinex1=8x_1 = 8
  4. Solve for y-coordinate: Solve for the y-coordinate of point V.\newlineUsing the y-coordinate of the midpoint, we have:\newline4=y1+824 = \frac{y_1 + 8}{2}\newlineMultiply both sides by 22 to clear the fraction:\newline8=y1+88 = y_1 + 8\newlineSubtract 88 from both sides to solve for y1y_1:\newliney1=88y_1 = 8 - 8\newliney1=0y_1 = 0
  5. Combine Coordinates: Combine the coordinates to form the point VV. We have found that the xx-coordinate of VV is 88 and the yy-coordinate of VV is 00. Therefore, the coordinates of point VV are (8,0)(8, 0).

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